The present invention relates to an electrical connector, and particularly to a PGA (Pin Grid Array) socket for connecting an integrated circuit package to a circuit board. An electrical connector, such as the disclosure of Taiwan Patent Application No.82602428, lowers the insertion force when conductive contacts of an integrated circuit package are inserted into the connector. Referring to FIG. 1, the conventional electrical connector includes a cover 2 and a base 3, and a conductive contact 31 is received in a hole 32 of the base 3. When an outer terminal 11 of an integrated circuit package 1 is inserted into a leading hole 21 of a cover 2, then the terminal 11 will be leaded to the hole 32 of the base 3 to electrically contact with a conductive contact 31 .The disclosed electrical connector uses the elasticity of the conductive contacts 3 to connect with terminals 11 of the IC package. Although the conventional contacts have a short conduction length, the contact elasticity thereof is limited by a receiving space of the electrical connector, thus reliable contact cannot be provided. Although the conventional contacts provide a reliable engagement, each contact has a long conduction length thereby leading to low conductive efficiency. Hence, there is a need for an electrical connector which provides reliable electrical contact and has a short conduction length.